Persistence length convergence and universality for the self-avoiding random walk

In this study, we show the convergence and new properties of persistence length, , for the self-avoiding random walk model (SAW) using Monte Carlo data. We generate high precision estimates of several conformational quantities with a pivot algorithm for the square, hexagonal, triangular, cubic and diamond lattices with path lengths of 103 steps. For each lattice, we accurately estimate the asymptotic limit , which corroborates the convergence of to a constant value, and allows us to check the universality on the curves. Based on the estimates we make an ansatz for dependency with lattice cell and spatial dimension, we also find a new geometric interpretation for the persistence length.